A129749 Numbers k that divide the sum of the first k nonprimes.

1, 8, 32, 44, 577, 5066, 5669, 8615, 39787, 59689, 109752, 146328, 15451380, 22173220, 28558717, 332573533, 1837410366, 3289933379, 19053646133, 370648112641

Offset: 1

Author

J. M. Bergot, May 14 2007

Keywords

• nonn
• more

Comments

A variant of A045345 and A053781.

a(21) > 10^12. - Donovan Johnson, May 20 2010

Examples

			The sum of the first 44 nonprimes is 1452 = 33*44.
		

Crossrefs

Cf. A045345 (n divides sum of first n primes), A053781 (n divides sum of first n composites), A018252 (nonprimes), A051349 (sum of first n nonprimes).

Programs

Maple

np:=proc(j) if isprime(j)=false then j else fi end: NP:=[seq(np(j),j=1..50000)]: a:=proc(n) if type(add(NP[j],j=1..n)/n,integer)=true then n else fi end: seq(a(n),n=1..nops(NP)); # Emeric Deutsch, May 16 2007

Mathematica

Module[{nn=150000,np},np=Accumulate[Select[Range[nn],!PrimeQ[#]&]];Select[Thread[ {np,Range[Length[np]]}],Mod[#[[1]],#[[2]]]==0&]][[;;,2]] (* The program generates the first 11 terms of the sequence. To generate more, increase the nn constant. *) (* Harvey P. Dale, Jan 04 2024 *)

Extensions

Edited and a(5) to a(18) added by Klaus Brockhaus, May 17 2007

a(19) from Donovan Johnson, Sep 19 2009

a(20) from Donovan Johnson, May 20 2010